Device having high-gradient magnetic cusp geometry



Jan. 18, 1966 R. A. DANDL ET AL 3,230,418

DEVICE HAVING HIGH-GRADIENT MAGNETIC GUSP GEOMETRY Filed June 25, 1961 3Sheets-Sheet l OUTER OUTER MIRROR ew INNER INNER MIRROR MIRROR COIL COILI Z- AXIS OUTER OUTER MIRROR MIRROR COIL COIL INNER INNER MIRROR MIRRORCOIL COIL Z AXIS 3! INVENTOR.

Raphael A. Dandl y Robe/"1 J. Kerr ATTORNEY Jan. 18, 1966 R A. DANDLETAL 3,230,418

DEVICE HAVING HIGH-GRADiENT MAGNETIC CUSP GEOME'IRY Filed June 25, 19615 Sheets-Sheet 2 u ['0 1; LO 0 070 NW) GUN PLASMA TO VACUUM PLASMATRAPPING REGION F i g. 2

PLASMA TO VACUUM INVENTOR. Raphael A. Dand/ y Roberf J. Kerr ATTORNEYJan. 18, 1966 A. DANDL ET AL 3,230,418

DEVICE HAVING HIGH-GRADIENT MAGNETIC GUSP GEOMETRY Filed June 23, 1961 3Sheets-Sheet 3 OUTER OUTER MIRROR MIRROR COIL COIL INNER INNER MIRRORMIRROR cOII COIL H z AxIs I ZERO 3 FIELD REGIONS 43 OUTER OUTER MIRROR41 EEQER TK MIRROR COIL CO|L MICROWAVE CAVITY 7 ELECTRON 45 HEATING z EINNER INNER MIRROR MIRROR COIL COIL 4 2 was PLASMA TRAPPING ZONEMIcROwAvE 49 RADIO FREQUENCY INVENTOR- SOURCE Raphael A. Dandl By RoberfJ. Kerr ATTORNEY United States Patent 3,230,418 DEVICE HAVINGHIGH-GRADIENT MAGNETTC CUSP GEOMETRY Raphael A. Band], Gal; Ridge, andRobert J. Kerr, Knoxviile, Tenn, assignors to the United States ofAmerica as represented by the United States Atomic Energy CommissionFiled June 23, 1961, Ser. No. 119,247 7 Claims. (Cl. 315--111) Thisinvention relates to a device for providing an improved magnetic fieldconfiguration possessing cusps for the containment of plasmas. Containedplasmas are desired in experimental study of controlled thermonuclearreactions, in experimental devices for study of the physics of plasmas,and as sources of neutrons, among other uses.

In most systems in which a plasma is confined by a magnetic field thatsurrounds it smoothly, i.e., without a discontinuity, there will be atendency toward instability. The reason is that the lines of force,which may be thought of as being stretched around the plasma, canshorten themselves by burrowing into the gas and thus force it outward.However, confinement which is substantially stable against arbitrarydeformation can be achieved if the field lines everywhere curve awayfrom a diamagnetic plasma, i.e., the field-plasma interface iseverywhere convex on the side toward the plasma. In order to satisfythis curvature requirement, the magnetic field configuration mustpossess cusps, i.e., points or lines (or both), through which the fieldlines pass outward from the center of the confinement region. Adiscussion of the energy principle for hydromagnetic stability iscontained in the Proceedings of the Royal Society, Series A, vol. 244,pp. 17-40, 1958.

Cusp geometries which have been developed in the past include the picketfence geometry and the chalice geometry. A discussion of these types ofgeometries is contained in the book by Samuel Glasstone and Ralph H.Lovberg entitled Controlled Thermonuclear Reactions, D. Van NostrandCompany, Inc., Princeton, New Jersey, pp. 421-427 (1960).

Two important features of any magnetic field configuration for thecontainment of plasmas are the inherent stability of the plasma and theadequate confinement of the plasma by the magnetic field. Prior art cuspconfigurations have in general been substantially stable devices.However, some of the plasma particles would not be confined by theseconfigurations since they would leak out by squeezing between the linesof the radial components of the magnetic field. Even with a plasma ofhigh density, the leakage rate would be excessive.

Under experimental thermonuclear conditions, a plasma behaves much likean ordinary gas, and exerts an outward pressure whose magnitudeincreases directly with the temperature and density. If a plasma is tobe confined, its outward pressure P must not exceed the inward pressureP which the magnetic field is capable of exerting. Since the plasma actslike a normal gas, P =nkT, where n is the particle density, T is thetemperature in K., and k is Boltzmanns constant. The maximum inwardpressure, P the magnetic field is capable of producing is given by B/81r, where B is the magnetic field strength in gauss. The ratio ofthese two pressures is denoted by [3, where ,B=nkT/(B /81r).

In order to provide a magnetic field configuration in which there are noradial components of the magnetic field, and such that a high value of B(approaching unity) could be realized, the present invention wasconceived. By a unique arrangement of magnetic mirror coils, an improvedcusp configuration is provided in which there Patented Jan. 18, 1966 isobtained a positive field gradient without radial field components. Thisfeature of the present invention substantially lowers the leakage rateof plasma particles which is inherent in conventional prior art cuspconfigurations. Thus, a higher density plasma may be magneticallycontained with the devices of the present invention and the containedplasma is confronted with an increasingly greater positive fieldgradient without radial components as it exerts a pressure thereagainstsuch that a high value of ,8 may be realized.

The improved cusp geometry of the present invention is oriented in sucha manner as to permit injection of a plasma along the field lines intothe low field region provided by this geometry, where the plasma will betrapped by collision with neutral gas molecules or with trapped ions.Plasma trapping in the low field region may also be achieved byproviding high energy electrons in the vicinity of this region. Theseelectrons will then generate a plasma by ionization of the backgroundgas.

It is the primary object of this invention to provide a positivehigh-gradient magnetic cusp field configuration possessing hydromagneticstability for the containment of plasmas.

It is another object of this invention to provide a device for producinga positive high-gradient magnetic cusp geometry in combination withmeans for forming a plasma in the low field region of the cusp geometry.

These and other objects and advantages of this invention will becomeapparent from a consideration of the following detailed specificationand the accompanying drawings wherein:

FIG. 1 is a schematic drawing of the arrangements of magnetic coils forthis invention and a plot of one form of the resultant magnetic cusps;

FIG. 2 is a schematic drawing of an arrangement of components forproducing a plasma in the magnetic field geometry of FIG. 1;

FIG. 3 is a schematic drawing of a variation of the magnetic fieldconfiguration of FIG. 1;

FIG. 4 is a schematic drawing of another variation of the magnetic fieldconfiguration of FIG. 1; and

FIG. 5 is a schematic drawing of another arrangement of components forproducing a plasma in the magnetic field geometry of FIG. 1.

The above objects have been accomplished in the present invention byproviding a pair of concentric coils spaced from another pair ofconcentric coil-s. Each outer coil is energized to provide a magneticfield reinforcing the other while the inner coils are energized toprovide a magnetic field directed opposite to that of the outer coils.The field configuration provided by the coils may be thought of as twoopposing magnetic mirrors. The resultant magnetic field produces pointcusps and line cusps. With a proper adjustment of coil current, one ormore low field regions can be achieved in the center of the devicebetween the pairs of concentric coils. Means are provided for injectinga plasma into the low field region for trapping therewithin, or forforming and trapping a plasma within this region by the use of energeticelectrons for ionizing the background gas.

FIG. 1 illustrates one embodiment of this invention in which theprinciples thereof may be carried out. An inner annular mirror coil 1 isencompassed by an outer annular mirror coil 2 in spaced relationthereto. Spaced from coils 1 and 2 are another pair of concentric,annular mirror coils 3 and 4. The coils 1, 2, 3 and 4 are energized withsources of DC. current in the same manner as are the coils 15, 17 and16, 18 of FIG. 2. The inner coils 1 and 3 are energized with about threetimes as much current as the outer coils 2 and 4 to provide a null orlow field region as shown on the drawing. Each of the outer coils 2 and4 is energized in such a way as to provide a magnetic field reinforcingthe other, while the inner coils 1 and 3 are energized to provide amagnetic field directed opposite to that of the outer coils. Themagnetic field lines are shown partially by the lines 6, 7, 8 and 9. Itcan be seen that the resultant magnetic field configuration produces twopoint cusps along the field Z axis and line cusps that followapproximately along 45 lines from the Z axis and the magnetic fieldlines forming the line cusps will pass between the inner and outercoils, as shown.

The device of FIG. 1 will have a positive field gradient in a planewhich passes through the center of region 5 and which is parallel to theinner faces of coils 1, 2 and 3, 4. This field gradient does not haveany radial components beyond the region 5 and the presence of such agradient will provide for the containment of a high density plasma in amanner such as set forth in FIG. 2, to be described below.

The device of FIG. 1 is enclosed in any suitable vacuum chamber, such asshown in FIG. 2, which is evacuated to a pressure of about 3 10-' mm.Hg. This pressure is not critical, but is given only as an example. Themagnetic field at the outer convex boundaries of the region 5 ismaintained at an average flux density of about 3500 gauss, for example.This flux density may be made higher, if desired, by adjusting thecurrent flow to the coils 1, 2, 3 and 4.

The device of FIG. 1 may be used as a means for the confinement of aconcentrated, energetic plasma in the low field region. FIG. 2illustrates one embodiment in which energetic, high density plasma maybe injected into the magnetic volume of FIG. 1. In FIG. 2, an innerannular magnetic mirror coil is encompassed by an outer annular magneticmirror coil 16. A plasma gun 35 is coaxially positioned between thecoils 15 and 16, as shown. The plasma gun 35 includes an anode 20, acathode 21, and an electrically floating electrode 22. An annularinsulator 23 is positioned between the electrode 22 and anode 20, and anannular insulator 24 is positioned between the electrode 22 and thecathode 21. The anode and cathode 21 are connected across an adjustablesource of operating potential 60 by means of a switch 61. Gas, from asource not shown, is fed to the arc discharge chamber manifold of thegun 35 through passageways and 26. The details of the operation of theion gun are fully set forth in the application of Raphael A. Dandl,Serial No. 18,461, filed March 29, 1960, now US. Patent No. 3,005,931,issued October 24, 1961. As set forth in the aforementioned application,the ion gun will produce a plasma of about 3 10 particles/ cc. in a 3000gauss magnetic field and with an operating voltage of about 1800 voltsbetween the anode and cathode. The plasma from the ion gun isuncontaminated by neutral particles. The plasma density of the plasmaprovided by the ion gun varies nearly proportionally to the square ofthe magnetic field strength. For a more complete description of the iongun and its operation, reference is made to the aforementionedapplication.

Spaced from the coils 15 and 16 and the ion gun 35 are a second pair ofconcentric inner and outer magnetic mirror coils 17 and 18 and a secondion gun 36 disposed in the space between the inner and outer coils 17and 18. The ion gun 36 includes an anode 27, a cathode 28, and anintermediate, electrically floating electrode 29. An

,annular insulator 31 is positioned between electrode 29 and anode 27,and an annular insulator 30 is positioned between electrode 29 andcathode 28. The anode 27 and cathode 28 are connected across anadjustable source of operating potential 62 by means of a switch 63. Gasfrom a source, not shown, is fed to the manifold of the ion gun 36through passageways 32 and 33. The ion gun 36 operates in the samemanner as the ion gun and as more fully set forth in the aforementionedapplication.

The magnetic field configuration of FIG. 2 is established in the samemanner as in FIG. 1 described above, that is, each of the outer coils16, 18 is energized to provide a magnetic field reinforcing the other,while the inner coils 15, 17 are energized to provide a magnetic fielddirected opposite to that of the outer coils. The outer coils 16, 18 areeach connected to a battery 54 and an adjustable resistor 56 by means ofa switch 55. The inner coils 15, 17 are each connected to a battery 57and an adjustable resistor 59 by means of a switch 58. By adjustment ofthe adjustable resistors 56 and 59, the inner coils 15, 17 are energizedwith about three times as much current as the outer coils 16, 18. Thedevice of FIG. 2 is enclosed in a suitable vacuum chamber 53 which isconnected to vacuum pumps, not shown, through the openings shown in thechamber 53. A dense, neutralized plasma 37 is injected from the ion gun35, and this plasma follows the field lines into the plasma trappingregion 19. Also, a dense, neutralized plasma 38 is injected from the iongun 36, and this plasma follows the field lines into the plasma trappingregion 19. The region 19 of FIG. 2 is the low-field region establishedby the coils 15, 16, 17 and 18. The plasma trapped in the region 19 willbe substantially stable against arbitrary deformation because of thefield lines everywhere curving away from the plasma in this region. Thepositive field gradient beyond region 19 in a plane through this region,as discussed for FIG. 1 above, will provide for containment of a highdensity plasma within this region. Since there are no radial componentsto this positive field gradient, the plasma will be adequately containedwithinregion 19 without any serious losses through the cusps, and theplasma will be hydromagnetically stable with a high value of the ratio,8. The resultant plasma confined in region 19 may then be useful as abreakup center for molecular ions or for other uses common to suchplasmas. When used as a breakup center for molecular ions, the particledensity and the particle energy will then be sufiicient for producing aquantity of neutrons in the region 19. The device of FIG. 2 is alsouseful in the experimental study of controlled thermonuclear reactions.

Variations of the basic axial cusp configuration of FIG. 1 and FIG. 2may be produced by changing the current in one of the sets of mirrorcoils to change the location and shape of the low or null field region.FIG. 3 and FIG. 4 are examples of such variations. Concentric inner andouter magnetic mirror coils 1' and 2' are spaced from concentric innerand outer magnetic mirror coils 3' and 4'. A partial showing of themagnetic field lines is shown by the lines 6', 7, 8' and 9. In FIG. 3current in the inside mirror coils 1 and 3 has been increased above thatused in FIG. 1 while the current in coils 2' and 4' remains the same asin FIG. 1, such that the null or low field is now a circle or toruscentered on the Z axis. In FIG. 4 the current in the outer mirror coils2' and 4' has been increased above that used in FIG. 1, While thecurrent in coils 1' and 3 remains the same as in FIG. 1, such that thereare two regions of null or low field on the Z axis equidistant from themidplane of the mirror coils. In either of these alternative fieldconfigurations, it will be possible to create and maintain a plasma inthe same manner as set forth for FIG. 2 above.

FIG. 5 illustrates another embodiment in which a plasma may be formed.In FIG. 5, an inner annular mirror coil 40 is encompassed by an outerannular mirror coil 41 in spaced relation thereto. Spaced from coils 40and 41 are another pair of concentric, annular mirror coils 42 and 43.The coils 40, 41, 42 and 43 are energized with sources of D.C. currentin the same manner as are the coils 15, 17 and 16, 18 of FIG. 2. Theinner coils 40 and 42 are energized With about three times as muchcurrent as the outer coils 41 and 43. Each of the outer coils 41 and 43is energized in such a way as to provide a magnetic field directedopposite to that of the inner coils 40, 42 to form a low field region44.

The device of FIG. 5 is enclosed in any suitable vacuum chamber such asshown in FIG. 2 and evacuated in the same manner as the device of FIG.2. A plasma may be formed in the device of FIG. 5 in the followingmanner. A microwave cavity 51 is placed at the center of the field, asshown in the drawing, for heating the electrons therein at theircyclotron frequency. The walls of this cavity 51 are perforated. Amicrowave radio frequency source 49 is connected to the cavity 51through a wave guide 50. The cavity 51 in combination with source 49 andthe wave guide 50 will provide an annular resonance volume 52 as shownon the drawing. The resonance volume is an annulus because the magneticfield is cylindrically symmetric. The cross section of this volume 52 isnot truly circular but is shown in this manner for the sake ofillustration. The heated electrons at their cyclotron frequency aretrapped Within the resonance volume 52. These electrons process incircular orbits within the annular volume 52, such that there are tworesultant circulating electric currents parallel to the axis of thevolume 52. These currents are directed in opposite directions, one alongthe inner periphery of the volume 52 and the other along the outerperiphery of the volume 52. Before the microwave source is energized,the magnetic field configuration of FIG. 5 is the same as the cuspconfiguration of FIG. 1 and is provided with a low field region 44.After the microwave source is energized to produce the annulus oftrapped hot electrons, the field produced by the trapped electrons willmodify the axial cusp configuration to provide a resultant fieldconfiguration with the low field region 44 being extended to encompassthe annular resonance volume 52 as shown in FIG. 5. The low field region44 which is extended to encompass the resonance volume 52 will bemaintained partially by the mirror coils and partially by thediamagnetic plasma formed in region 44 by the ionization of thebackground gas by the heated electrons therein. The directions of themagnetic field lines of the resultant field configuration are shownpartially by the lines 45, 46, 47 and 48. The magnetic field strength isso chosen that the electron cyclotron frequency in a zone inside thecavity 51 is the same as the injected radio frequency. The injectedradio frequency may be about 225K mc., for example.

The energetic electrons in the resonance volume 52 will absorb an energydepending on their residence time and the applied field strength, andwill ionize the background gas. The plasma thus formed is then containedin the cusped low field containment zone 44 encompassing the resonancevolume. The above method of plasma formation and trapping can be usedseparately or in conjunction with the coaxial plasma guns of FIG. 2.When used together, the plasma guns and the resonant cavity method wouldsupplement each other in the formation and containment of an energeticplasma in the containment zone 44 of FIG. 5.

This invention has been described by way of illustration rather thanlimitation and it should be apparent that this invention is equallyapplicable in fields other than those described.

What is claimed is:

1. An improved means for providing a magnetic field configurationpossessing cusps comprising a first pair of concentric inner and outermagnetic mirror coils, a second pair of concentric inner and outermagnetic mirror coils, spaced apart and in alignment with said firstpair of coils, said coils being enclosed within an evacuated enclosure,means for energizing each of said outer coils to provide a fieldreinforcing the other, and means for energizing said inner coils toprovide a field directed opposite to that provided by the outer coils,the combined effects of said fields producing a resultant magnetic fieldwith at least one low field region in the center of the space betweenthe pairs of coils, said low field region being bounded by line cuspsand point cusps.

2. The improved means set forth in claim 1, wherein said inner coils areenergized with a first, predetermined magnitude of current, and saidouter coils are energized with a second, predetermined magnitude ofcurrent to provide a magnetic field strength at the boundary of said lowfield region of about 3500 gauss average flux density.

3. The improved means set forth in claim 2, wherein said first currentis about three times larger than said second current.

4. The improved means set forth in claim 3, wherein said first currentis increased while said second current remains the same to increase thedifference between said currents to thus provide said low field regionin the form of a torus.

5. The improved means set forth in claim 3, wherein said second currentis increased while said first current remains the same to decrease thedifference between said currents to thus provide a pair of low fieldregions equidistant from the midplane of the pairs of concentric mirrorcoils.

6. The improved means set forth in claim 3, and further including afirst ion gun disposed between the inner and outer magnetic mirror coilsof said first pair of concentric coils, a second ion gun disposedbetween the inner and outer magnetic mirror coils of said second pair ofconcentric coils, means for actuating said ion guns to provide anenergetic, neutral plasma with a density of at least 3X10 particles/cc.from each of said guns, said plasma following the field lines providedby said coils into said low field region where said plasma ismagnetically trapped, wherein said plasma in said region issubstantially stable against arbitrary deformation.

7. The improved means as set forth in claim 3, and further including amicrowave resonant cavity encompassing said low field region, amicrowave radio frequency source, and a wave guide connected betweensaid source and said cavity for providing an annular resonance volumewithin said cavity for heating electrons therein at a cyclotronfrequency equal to the frequency of said source, said heated electronsproducing a field which modifies the existing field configuration toprovide a resultant low field region which encompasses said resonancevolume, the electrons in said resonance volume ionizing the backgroundgas within said cavity to thus form a plasma which is magneticallytrapped within said resultant low field region.

References Cited by the Examiner UNITED STATES PATENTS 3,038,099 6/1962Baker et al. 315-111 X 3,069,344 12/ 1962 Post et al. 3l5-111 X3,170,841 2/1965 Post 315-1l1 X GEORGE N. WESTBY, Primary Examiner.

C. R. CAMPBELL, D. E. SRAGOW,

Assistant Examiners.

1. AN IMPROVED MEANS FOR PROVIDING A MAGNETIC FIELD CONFIGURATIONPOSSESSING CUSPS COMPRISING A FIRST PAIR OF CONCENTRIC INNER AND OUTERMAGNETIC MIRROR COILS, A SECOND PAIR OF CONCENTRIC INNER AND OUTERMAGNETIC MIRROR COILS, SPACED APART AND IN ALIGNMENT WITH SAID FIRSTPAIR OF COILS, SAID COILS BEING ENCLOSED WITHIN EVACUATED ENCLOSURE,MEANS FOR ENERGIZING EACH OF SAID OUTER COILS TO PROVIDE A FIELDREINFORCING THE OTHER, AND MEANS FOR ENERGIZ-